At $T \ K$,the equilibrium constants for the following two reactions are given below:
$2 A_{(g)} \rightleftharpoons B_{(g)} + C_{(g)} ; K_1 = 16$
$2 B_{(g)} + C_{(g)} \rightleftharpoons 2 D_{(g)} ; K_2 = 25$
What is the value of equilibrium constant $(K)$ for the reaction given below at $T \ K$?
$A_{(g)} + \frac{1}{2} B_{(g)} \rightleftharpoons D_{(g)}$

• A
  $100$
• B
  $50$
• C
  $20$
• D
  $75$